With the progress of society and the improvement of living standards, people put forward more and higher requests for working and living environments and articles. Take chairs for example, office chairs or other chairs in diversified designs increasingly appear to meet people's different needs, such as a lifting regulation chair, a chair with a regulatable waist cushion, a chair with a regulatable headrest, a chair with a backrest in regulatable inclination and elevation, etc. However, for all kinds of chairs in the prior art, a backrest is directly connected or integrated with a seat or is connected with the seat by a support rod, and thus, for such chairs, even if the backrest can be regulated relatively to the seat, the backrest is regulated for angle change relatively to the seat, so as to be suitable for people to sit up and lean back. As yet, a chair with a backrest which can move back and forth relatively to a seat has not appeared.